A new method of simultaneous biometric verification and generation of a random number for use in authenticated encrypted communication is described. A non-linear transform is applied to a vector derived from a biometric. The output of the same dimension is fed back and the process iterated. At each iteration, the magnitude and phase of a scalar complexvalued inner product of the vector and its displacement from the previous iteration is extracted. It is shown that this product tends towards a certain limit along a trajectory in the complex plane. Both the limit and the trajectory depend on the initial condition which is the biometric vector. For close initial conditions the trajectories will initially remain close but separate exponentially. Magnitude and phase on the trajectory are converted into binary matrices. Entropy criteria are used to weight bits and verify identity. High entropy bits are selected for random number generation. The method was tested using 3D facial images from 61 persons in the Face Recognition Grand Challenge (FRGC) database. An Equal Error Rate of 15.5% was achieved and random numbers of length 512 bits could be generated that satisfied standard tests for randomness. The method can be further developed to generate private keys from low intra-class entropy bits and session keys from the unconditionally random bits on presentation of a biometric without the need to store them
